Inventory Management & EOQ: Costs, Models & Trade-offs

TAKEAWAYS:

• Inventory management balances ordering costs (fixed per order) and holding costs (storage, insurance, obsolescence) to optimize cash flow.
• The EOQ formula $EOQ=\sqrt{\frac{2DS}{H}}$ finds the order quantity that minimizes total inventory costs, where $D$ = annual demand, $S$ = ordering cost, and $H$ = holding cost per unit.
• Safety stock is held to prevent stockouts from demand variability or lead-time uncertainty, calculated as $\text{Safety Stock}=z\times \sigma \times \sqrt{L}$, where $z$ = safety factor, $\sigma$ = demand standard deviation, and $L$ = lead time.
• ABC analysis classifies inventory into three categories (A: high-value/low-quantity, B: medium, C: low-value/high-quantity) to prioritize management efforts.
• Real-world examples show how EOQ reduces costs for NTC’s spare parts, Daraz’s warehouse orders, and local grocery stores’ perishable goods.
• Exam questions often test EOQ calculations, cost trade-offs, and inventory classification with numerical data.

1. What is Inventory Management?

Inventory management is the process of ordering, storing, and using a company’s inventory efficiently to meet customer demand while minimizing costs. It involves:

• Controlling stock levels to avoid overstocking or stockouts.
• Tracking inventory (raw materials, work-in-progress, finished goods).
• Balancing costs: Ordering costs (e.g., placing orders, transportation) vs. holding costs (storage, insurance, spoilage).

Why is Inventory Important?

mindmap
  root((Why Inventory Matters?))
    --- Cash Flow
    --- Customer Satisfaction
    --- Operational Efficiency
    --- Risk Management
    --- Cost Control

2. Costs of Inventory

Inventory incurs two primary costs that managers must balance:

Key Insight:

• Ordering too frequently → High ordering costs.
• Ordering too infrequently → High holding costs.
• Optimal point = EOQ, where total costs are minimized.

3. The Economic Order Quantity (EOQ) Model

The EOQ model determines the optimal order quantity that minimizes total inventory costs (ordering + holding).

EOQ Formula

$$EOQ=\sqrt{\frac{2DS}{H}}$$ Where:

• $D$ = Annual demand (units)
• $S$ = Ordering cost per order (Rs.)
• $H$ = Holding cost per unit per year (Rs.)

Total Cost Equation

$$\text{Total Cost}=\left(\frac{D}{Q}\right)S+\left(\frac{Q}{2}\right)H$$ Where $Q$ = Order quantity.

Worked Example: Kathmandu Retail Shop

Scenario: A Kathmandu-based grocery shop sells 5,000 kg of rice annually.

• Ordering cost (S) = Rs. 200 per order (transport + paperwork).
• Holding cost (H) = 15% of rice cost = Rs. 10 per kg/year (rice costs Rs. 66.67/kg).
• Lead time = 2 weeks (no safety stock needed for this example).

Step 1: Calculate EOQ $$EOQ=\sqrt{\frac{2\times 5000\times 200}{10}}=\sqrt{200,000}=447\text{ kg (approx. 450 kg)}$$

Step 2: Calculate Total Cost at EOQ $$\text{Number of orders}=\frac{5000}{450}\approx 11.11\text{ orders/year}$$ $$\text{Ordering Cost}=11.11\times 200=\text{Rs. }2,222$$ $$\text{Holding Cost}=\frac{450}{2}\times 10=\text{Rs. }2,250$$ $$\text{Total Cost}=2,222+2,250=\text{Rs. }4,472$$

Step 3: Compare with Other Order Quantities

Conclusion: Ordering 450 kg per order minimizes total inventory costs to Rs. 4,472/year.

4. Assumptions of EOQ Model

The EOQ model simplifies reality with these assumptions:

1. Demand is constant and known.
2. Lead time is fixed (no delays).
3. Order quantity is received all at once (no partial deliveries).
4. No quantity discounts (price per unit is constant).
5. Stockouts are not allowed (infinite supply).

Real-World Adjustments:

• Safety Stock: Added for demand uncertainty (e.g., monsoon affecting agriculture).
• Reorder Point (ROP): Trigger for new orders = $\text{Average Daily Usage}\times \text{Lead Time}+\text{Safety Stock}$.
• Quantity Discounts: If bulk orders reduce per-unit cost, EOQ may change.

5. Inventory Classification: ABC Analysis

Not all inventory items require the same level of control. ABC analysis categorizes items based on annual consumption value:

Example: Daraz Warehouse

• A Items: Smartphones (high value, low quantity).
• B Items: Chargers (moderate value).
• C Items: Packaging materials (low value, high quantity).

6. Inventory Management Techniques

A. Just-in-Time (JIT) Inventory

• Goal: Receive goods only as needed for production/sales.
• Pros:
  • Reduces holding costs.
  • Improves cash flow.
• Cons:
  • Requires reliable suppliers.
  • Vulnerable to supply chain disruptions (e.g., COVID-19, natural disasters).
• Example: Toyota’s lean manufacturing uses JIT to minimize inventory.

B. Safety Stock

• Purpose: Prevent stockouts due to demand variability or lead-time uncertainty.
• Calculation: $$\text{Safety Stock}=z\times \sigma \times \sqrt{L}$$ Where:
  • $z$ = Safety factor (e.g., 1.65 for 95% confidence).
  • $\sigma$ = Standard deviation of demand.
  • $L$ = Lead time in days.

Example: NTC’s Spare Parts

• Annual demand = 10,000 units.
• Lead time = 5 days.
• Daily demand = 27.4 units ($\sigma =5$ units).
• Safety Stock = $1.65\times 5\times \sqrt{5}\approx 18.4$ units.

C. Economic Production Quantity (EPQ)

• Used when production is continuous (not instant like EOQ).
• Formula: $$EPQ=\sqrt{\frac{2DS}{H}\times \frac{P}{P-D}}$$ Where $P$ = Production rate.

7. Real-World Applications in Nepal

Example 1: Daraz’s Inventory Management

• Problem: Daraz faces high holding costs due to perishable goods (e.g., groceries, electronics).
• Solution:
  • Uses EOQ for non-perishables (e.g., books, home goods).
  • Implements JIT for perishables with short shelf life.
  • ABC analysis to prioritize high-value items (e.g., iPhones).

Example 2: NTC’s Spare Parts Inventory

• Challenge: Long lead times for importing spare parts.
• Strategy:
  • Maintains safety stock for critical parts (e.g., transformers).
  • Uses EOQ for frequently used items (e.g., cables, switches).
  • Vendor managed inventory (VMI): Suppliers monitor stock levels.

Example 3: Kathmandu Grocery Store (Perishables)

• Issue: Milk and vegetables spoil quickly.
• Approach:
  • Daily ordering (high frequency, low quantity) to minimize holding costs.
  • No safety stock (orders based on same-day demand).
  • Local suppliers to reduce lead time.

8. Inventory Management in Functional Budgeting

Inventory decisions impact budgets in multiple ways:

1. Sales Budget: Stock levels affect ability to meet demand.
2. Production Budget: Raw material inventory influences production schedules.
3. Cash Flow Budget: Holding too much inventory ties up cash.

Example: Functional Budget for a Nepali Manufacturing Firm

Exam Tip: How to Score Full Marks

1. Understand the EOQ Formula:

   • Memorize $EOQ=\sqrt{\frac{2DS}{H}}$.
   • Always show calculations step-by-step in exams.

2. Distinguish Between Costs:

   • Ordering Cost vs. Holding Cost vs. Stockout Cost.
   • Example: "If ordering cost increases, EOQ will increase (since $S$ is in the numerator)."

3. Apply to Real Scenarios:

   • NTC: Use EOQ for spare parts.
   • Daraz: ABC analysis for product prioritization.
   • Local Shop: JIT for perishables.

4. Common Exam Questions:

   • Calculate EOQ given $D,S,H$.
   • Compare total costs at different order quantities.
   • Explain ABC analysis with an example.
   • Discuss advantages/disadvantages of JIT.

5. Avoid These Mistakes:

   • Ignoring units (e.g., mixing kg and units).
   • Forgetting to annualize (e.g., using monthly demand instead of yearly).
   • Assuming no safety stock when demand is variable.

flowchart TD
    A["Start: Demand Forecast"] --> B["Determine Ordering Cost (S) and Holding Cost (H)"]
    B --> C["Calculate EOQ: √(2DS/H)"]
    C --> D["Decide Order Quantity"]
    D --> E["Set Reorder Point: (Daily Usage × Lead Time) + Safety Stock"]
    E --> F["Place Order"]
    F --> G["Receive Inventory"]
    G --> H["Monitor Inventory Levels"]
    H -->|"Stock Low?"| E
    H -->|"Stock High?"| I["Adjust Order Quantity or Safety Stock"]
    I --> C

Caption: The Inventory Management Cycle (EOQ-Based)